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Complex Numbers

If α and ...

Question

If $α$ and $β$ are zeros of quadratic equation $f (x) = x^{2} - p x + q$ , then find the values of the following:
$α^{2} + β^{2}$

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Solution

Given $α$ and $β$ are zeros quadratic equation $f (x) = x^{2} - p x + q$
$∴ α + β = - (\frac{- p}{1}) = p$
and $α = \frac{q}{1} = q$
$α^{2} + β^{2} = (α + β)^{2} - 2 α β$
$= p^{2} - 2 q$

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